Whakaoti i te frac{sqrt{75}-sqrt{18}}{sqrt{12}}

$$\frac { \sqrt { 75 } - \sqrt { 18 } } { \sqrt { 12 } }$$

Aromātai

$$\frac{5-\sqrt{6}}{2}\approx 1.275255129$$

Ngā Upane Otinga

Tauwehea te 75=5^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 3} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{3}. Tuhia te pūtakerua o te 5^{2}.

$$\frac{5\sqrt{3}-\sqrt{18}}{\sqrt{12}}$$

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{5\sqrt{3}-3\sqrt{2}}{\sqrt{12}}$$

Tauwehea te 12=2^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 3} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{3}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{5\sqrt{3}-3\sqrt{2}}{2\sqrt{3}}$$

Whakangāwaritia te tauraro o \frac{5\sqrt{3}-3\sqrt{2}}{2\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{\left(5\sqrt{3}-3\sqrt{2}\right)\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\left(5\sqrt{3}-3\sqrt{2}\right)\sqrt{3}}{2\times 3}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{\left(5\sqrt{3}-3\sqrt{2}\right)\sqrt{3}}{6}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5\sqrt{3}-3\sqrt{2} ki te \sqrt{3}.

$$\frac{5\left(\sqrt{3}\right)^{2}-3\sqrt{2}\sqrt{3}}{6}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{5\times 3-3\sqrt{2}\sqrt{3}}{6}$$

Whakareatia te 5 ki te 3, ka 15.

$$\frac{15-3\sqrt{2}\sqrt{3}}{6}$$

Hei whakarea \sqrt{2} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{15-3\sqrt{6}}{6}$$